Muntz-type theorems on the half-line with weights

TL;DR

This paper investigates conditions under which the linear span of certain weighted functions is dense in weighted L2 spaces, providing new necessary and sufficient criteria and comparing them with existing results.

Contribution

It introduces new necessary and sufficient conditions for density of function spans in weighted L2 spaces, expanding the theoretical understanding of Muntz-type theorems.

Findings

Established a necessary condition for density

Provided a sufficient condition for density

Compared new results with existing literature

Abstract

We consider the linear span S of the functions tak (with some ak > 0) in weighted L2 spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comparisons are also made between the new results and those that can be deduced from older ones in the literature.